MinT - Best Known (81−68, 81, s)-Nets in Base 16

Best Known (81−68, 81, s)-Nets in Base 16

(81−68, 81, 65)-Net over F₁₆ — Constructive and digital

Digital (13, 81, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 81, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(81−68, 81, 97)-Net over F₁₆ — Digital

Digital (13, 81, 97)-net over F₁₆, using

net from sequence [i] based on digital (13, 96)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 13 and N(F) ≥ 97, using
  - a curve from the manYPoints database [i]

(81−68, 81, 648)-Net in Base 16 — Upper bound on s

There is no (13, 81, 649)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 35 586647 620371 473337 653577 294302 506765 834235 308723 525437 382324 342211 451165 699829 399763 722958 001616 > 16⁸¹ [i]